{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:E55V4LH3KIEDGVMAOZOVCO5C2F","short_pith_number":"pith:E55V4LH3","schema_version":"1.0","canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","source":{"kind":"arxiv","id":"2606.29679","version":1},"attestation_state":"computed","paper":{"title":"Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Igor Halperin","submitted_at":"2026-06-29T00:57:57Z","abstract_excerpt":"Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \\times N$ distance matrix $M(t)$ on a held set of $N$ inputs. OMD uses methods of random matrix theory and particle dynamics to explore spectral reorganisations that are missed by scalar loss functions, but are informative of the training process. We read $M(t)$ against a perturbative ambient-versus-latent decomposition extending the Bogomolny--Bohigas--Schmit (BBS) theory of random distance matrices, with per-snapsho"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.29679","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cs.LG","submitted_at":"2026-06-29T00:57:57Z","cross_cats_sorted":[],"title_canon_sha256":"42e2ec0e7b4bd659c68dee7d3822de0e0d926ee51b276fa4ed3d0e1e7ba9b6c4","abstract_canon_sha256":"2be14948b4e1f20f16484dd127217b5454f8fb7c2c4252be775735070eba057f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:17:30.407831Z","signature_b64":"n0A12tQp6Y5wjgt1YntfI7OhFsYUUO3SmXKkv2CN9gCAYZofEzpfTdVXOfkVfC8WX2g7Aa7yPvCH3RjrQaX3Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"277b5e2cfb5208335580765d513ba2d1631a0a98112a3fb1f31c08dc619daea0","last_reissued_at":"2026-06-30T02:17:30.407327Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:17:30.407327Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Learning as Observable Matrix Dynamics: Diffusive Relaxations versus Phase Transitions","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Igor Halperin","submitted_at":"2026-06-29T00:57:57Z","abstract_excerpt":"Observable Matrix Dynamics (OMD) is a diagnostic framework that probes the dynamics of high-dimensional internal representations of inputs by a neural network via a fixed-size $N \\times N$ distance matrix $M(t)$ on a held set of $N$ inputs. OMD uses methods of random matrix theory and particle dynamics to explore spectral reorganisations that are missed by scalar loss functions, but are informative of the training process. We read $M(t)$ against a perturbative ambient-versus-latent decomposition extending the Bogomolny--Bohigas--Schmit (BBS) theory of random distance matrices, with per-snapsho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29679","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29679/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.29679","created_at":"2026-06-30T02:17:30.407393+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.29679v1","created_at":"2026-06-30T02:17:30.407393+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29679","created_at":"2026-06-30T02:17:30.407393+00:00"},{"alias_kind":"pith_short_12","alias_value":"E55V4LH3KIED","created_at":"2026-06-30T02:17:30.407393+00:00"},{"alias_kind":"pith_short_16","alias_value":"E55V4LH3KIEDGVMA","created_at":"2026-06-30T02:17:30.407393+00:00"},{"alias_kind":"pith_short_8","alias_value":"E55V4LH3","created_at":"2026-06-30T02:17:30.407393+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F","json":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F.json","graph_json":"https://pith.science/api/pith-number/E55V4LH3KIEDGVMAOZOVCO5C2F/graph.json","events_json":"https://pith.science/api/pith-number/E55V4LH3KIEDGVMAOZOVCO5C2F/events.json","paper":"https://pith.science/paper/E55V4LH3"},"agent_actions":{"view_html":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F","download_json":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F.json","view_paper":"https://pith.science/paper/E55V4LH3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.29679&json=true","fetch_graph":"https://pith.science/api/pith-number/E55V4LH3KIEDGVMAOZOVCO5C2F/graph.json","fetch_events":"https://pith.science/api/pith-number/E55V4LH3KIEDGVMAOZOVCO5C2F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/action/storage_attestation","attest_author":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/action/author_attestation","sign_citation":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/action/citation_signature","submit_replication":"https://pith.science/pith/E55V4LH3KIEDGVMAOZOVCO5C2F/action/replication_record"}},"created_at":"2026-06-30T02:17:30.407393+00:00","updated_at":"2026-06-30T02:17:30.407393+00:00"}